In microprocessor-based protective relays, such as used for protection of electric power systems, a pair of numerical filters is typically used to compute the complex numbers which represent the fundamental component phasors for the power system voltage and current waveforms. The phasors are used by the protective relay to carry out its monitoring and protection functions for the power system. The numerical filters are designed so that their output waveforms are orthogonal, which reduces the impact of waveform harmonics and DC offsets. Typically, digital finite impulse response (FIR) filters are used in this arrangement. One FIR filter output represents the real part of the complex number for the phasor, while the output of the other FIR filter represents the imaginary part of the complex number.
The filters are designed such that at the rated frequency of the power system, i.e. 60 or 50 Hz, depending on the particular country, the gain of each filter is unity and the phase angle between the two outputs is 90°, i.e. orthogonal. However, when the actual power system frequency is different than the rated frequency, the phasor (produced by the two filters) will have errors, both in magnitude and in phase angle; these errors become larger as the actual power signal frequency deviates further from the rated frequency. Errors in the phasors are undesirable, as they can result in erroneous/poor performance of the protective relay.
Although various techniques are known and have been used to compensate for fundamental component phasor errors resulting from differences between the actual frequency and the rated frequency, one well-known and frequently used technique, known generally as frequency tracking, adjusts the number of samples per cycle (the sampling frequency) for the incoming power signal depending on line difference between the actual and rated frequencies. The frequency of the incoming power signal (the actual power system frequency) is measured and the sampling frequency is adjusted accordingly.
Another technique, based on a fixed sampling rate, is described in U.S. Pat. No. 6,141,196 to Premerlani, which corrects the phasor obtained from the filtering system by introducing two correction factors, referred to in Premerlani as ε1 and ε2. The correction factors are used in the following equation, where Zm is equal to the corrected phasor and Xm is the measured (actual) phasor.{overscore (Z)}m=(1+ε2−ε1){overscore (X)}mThe Premerlani ε1 and ε2 values are calculated using specific equations set out in Premerlani, which include values of actual (measured) system frequency and rated frequency. However, the Premerlani technique, while providing some correction for phasor errors due to frequency difference, still results in phasors which include some error. The amount of the error increases as the frequency difference increases. Further, the Premerlani technique is applicable only to full cycle Fourier-type FIR filters. It cannot be used for other FIR filters, such as Cosine filters.
Hence, it would be desirable to have a compensation system which provides an exact compensation for phasors when the measured power system frequency is different from the rated frequency, and further that such a compensation system provide such exact compensation over a wide range of frequency difference.